No wonder, Infinity is quite a controversial term in the mathematical world, though it includes so many interesting yet bizarre facts in it. Wanna know about those facts let’s explore it here.
Number, character, symbol, units, etc are some of the significant parts of our lives. We cannot even visualize our basic needs allied studies, career and daily chores without maths. That is probably one of the important reason why mathematics proves to be an essential subject for students.
Well, maths can be scary at times, but if learned properly and with fun, they can be pretty amazing and cool. It gives us so many fundamental things such as Pie, shape, character, symbol, zero and Infinity.
Infinity is a mathematical concept that is beyond all the numbers, or in addition, we can say that it is larger than any natural number.
In the late 19th and early 20th centuries, German mathematician Georg Cantor formalized many ideas allied to infinity. From that time, Infinity was known as the important segment of the Mathematics world. The concept of infinity actually holds so many facts some are really interesting and fun while on the other hand, some are pretty weird.
Here are the 11 weirdest things allied to infinity.
Everyone has, at their childhood, found themselves in a contest to declare the largest number. Well, it was really fun as it starts off with perhaps a hundred, or a thousand, then a million, a billion, a trillion and lot more.
The decision seems like never ending then, you decide it's time to pull out your trump card: infinity! Because infinity plus any number is equal to infinity. But how can you miss Hilbert’s hotel paradox?
But, this infinity puzzle actually bestows this oneplus concept. According to that puzzle if a hotel that has an infinite number of rooms. A person arrives and requests a room hotel staff informed that all of the rooms are occupied. But, the hotel has infinite rooms so how can the hotel not have any more rooms. What should a person do now?
Well, according to that puzzle this can be done by moving the guest in room 1 to room 2, the guest in room 2 to room 3, and so on. When all guests have moved, room 1 is empty, and the new person can use it. In general, the fact can be formalized as room n will be moved to room n+1.
We have learned since childhood that one minus one equals to zero, (same number minus same number is equals to zero) But, strangely the same formula doesn’t fit in Infinity. Well, the funda is equally confusing as the funda of [infinity] + 1 = [infinity]. Infinity minus infinity is undefined in the same way that dividing by zero is undefined.
Odd and Even are the two familiar term belongs to Mathematics. Well, how it is related to Infinity is again pretty confusing we must say. In general, infinity is an adjective used to describe any number whose magnitude is greater than that of all finite numbers.
Now infinite numbers include both odd and even numbers and there are infinite numbers which are not integers, and these latter values are not even and not odd.
As we know that Infinity is countless, boundless but it comes in different sizes. Strange it is, right? But, it is true. In the mathematical world the set of number those greater than 0 (Positive Numbers) and the set of the number those smaller than 0 (Negative Numbers) may be considered to be infinite sets of equal sizes.
These are two different sets but when you combine both the sets, you get a set twice as large. Another example is simply adding 1 to infinity. The number ∞ + 1 > ∞.
Obviously, in regular mathematics dividing by zero is a big no. It is an undefined expression basically. In usual scheme of things, the number 1 divided by 0 cannot be defined. But, when it comes to infinity there's more than one way to do the math. We can put it as Similarly, ∞/0=∞, but the answer ∞ is larger than question ∞. Like another strange fact!
Everyone is aware of the symbol of Infinity “∞”. But, few people know about its history. Well, the symbol is also known the lemniscate, was introduced by clergyman and mathematician John Wallis in 1655.
The word "lemniscate" is pretty strange that belongs to the Latin word lemniscus, which means "ribbon," while the word "infinity" comes from the Latin word infinitas, which means "boundless."
We have seen plus, we have seen minus, we have seen divide and multiplication also, these are the basic mathematical operation we performed. But, when you linked it to infinity then, the answer will always remain infinity. You can call it undefined but in general, you will get the single result and that will be infinity.
According to Georg Cantor a German mathematician, the infinite number of whole numbers (0, 1, 2, 3 . . . ) is smaller than the infinite number of irrational numbers.
In mathematics, the irrational numbers are numbers like pi includes a series of decimals that go on like infinite for example (3.1415632 . . . ). Cantor showed that the infinite number of irrational numbers is larger than that of the infinite number of whole numbers. These irrational numbers are countless in addition we can say that these infinite of an irrational number is actually greater than other numbers.
9) Many Levels of Infinity
Cantor also showed that, just as the number of infinite whole numbers is on a whole different level of infinity than the number of irrational numbers, there is also a type of infinity that is larger than the number of irrational numbers, a level of infinity above that, another one above that, and so on, up through (you guessed it) infinity. Furthermore, any level of infinity added to a higher level of infinity automatically sums to the higher level of infinity in the same way that infinity plus one equals infinity.
Another great fact about infinity is the number π or pi. Yes, Pi is an example of Infinity. In general, we use the phenomenon of pi because it's impossible to write huge range of numbers. Pi consists of an infinite number of digits. It's often rounded to many digits like 3.14 or even 3.14159, yet no matter how many digits, it is like never-ending process.
Obviously, we all have heard about the mathematical term fractal, it is an object used to explain and simulate naturally occurring objects. It is usually written as a mathematical equation, are nowhere differentiable. When it comes to observing an image of a fractal, this means you could zoom in and see new detail. In other words, a fractal is infinitely magnifiable. That’s how we can link the infinity term with fractal.
Theories had various ideas about the nature of infinity some are really meaningful and some are quite bizarre either way you have to go for it.
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